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Dec 30, 2015 at 3:07 comment added xzczd Interesting. Just a side note, one of the key point of this approach is the Method of GroebnerBasis can't be default i.e. Lexicographic.
Dec 29, 2015 at 15:55 comment added John McGee Your functions were rational but to solve f(x,y)=a it can be turned into a root problem by solving f(x,y)-a=0, then only the numerator if this expression matters. The Groebner basis is a set of polynomials that have the same roots, (zero set) but in a simplified form, much like Gaussian elimination simplifies a set of linear equations.
Dec 29, 2015 at 14:44 comment added George I don't have the knowledge to understand your answer but I will try to understand it. It looks very helpful. Thank you very much.
Dec 29, 2015 at 13:44 history answered John McGee CC BY-SA 3.0